Project Euler/java/P29.java
import java.math.BigInteger;
import java.util.ArrayList;

public class P29 {
	public static void main(String... args) {
		new P29();
	}

	public P29() {
		ArrayList<BigInteger> lista = new ArrayList<BigInteger>();
		BigInteger x, y;
		for (int a = 2; a < 101; ++a) {
			x = new BigInteger("" + a);
			for (int b = 2; b < 101; ++b) {
				y = x.pow(b);
				if (!lista.contains(y))
					lista.add(y);

			}
		}
		System.out.println(lista.size());
	}
}

/*
 * Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:
 * 
 * 22=4, 23=8, 24=16, 25=32
 * 32=9, 33=27, 34=81, 35=243
 * 42=16, 43=64, 44=256, 45=1024
 * 52=25, 53=125, 54=625, 55=3125
 * 
 * If they are then placed in numerical order, with any repeats removed, we get
 * the following sequence of 15 distinct terms:
 * 
 * 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
 * 
 * How many distinct terms are in the sequence generated by ab for 2 <= a <= 100
 * and 2 <= b <= 100?
 */